The Depreciation Multiplier - de Wolff, P. (The Review of Economics and Statistics, 1966)
ONE of the most comrmronly used methods of depreciating capital goods is to write off their initial value in equal annual portions in the course of the estimated lifetime. When this lifetime is correctly estimated and when the depreciation fund is left idle its value (apart from price changes which will be left entirely out of account here) at the end of the lifetime will evidently be equal to the initial value of the capital good and will allow for the replacement of the worn-out item by an exactly identical new one. In reality, this equality will very seldom be fulfilled. This is not only due to the fact that the individual lifetimes of identical capital goods will vary so that, at best, only a correct average can be used which could yield equality for very large values of the initial stock only, but still more because depreciation funds are usually reinvested in one way or another long before replacement has become necessary. In particular, in dynamic processes replacement and depreciation may differ considerably. Already in 1953 E. Doomar [2] has proved that in an exponentially growing economy, when depreciation funds are immediately reinvested, the method of constant depreciation over time will lead to an amount of depreciation D, at time t bearing a constant ratio to the amount to be replaced R,, given by: Dt: Rt = (eyT -1) :yT1 ) where y is the rate of growth of the economy and T the average lifetime of the capital goods. For reasonable values of y and T the ratio may differ greatly from one. Dr. Horvat [3] studies the consequences of the method for a different kind of dynamic process. He considers a large stock of identical new capital goods Ko at t= 0. All items are assumed to have exactly the same lifetime, T. Hence, according to the method of